• Steel and Composite Structures
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• v.42 no.6
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• pp.805-826
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• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.

• Steel and Composite Structures
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• v.43 no.1
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• pp.79-90
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• 2022

In this study, the dynamic behavior of functionally graded layered deep beams with viscoelastic core is investigated including the porosity effect. The material properties of functionally graded layers are assumed to vary continuously through thickness direction according to the power-law function. To investigate porosity effect in functionally graded layers, three different distribution models are considered. The viscoelastically cored deep beam is exposed to harmonic sinusoidal load. The composite beam is modeled based on plane stress assumption. The dynamic equations of motion of the composite beam are derived based on the Hamilton principle. Within the framework of the finite element method (FEM), 2D twelve -node plane element is exploited to discretize the space domain. The discretized finite element model is solved using the Newmark average acceleration technique. The validity of the developed procedure is demonstrated by comparing the obtained results and good agreement is detected. Parametric studies are conducted to demonstrate the applicability of the developed methodology to study and analyze the dynamic response of viscoelastically cored porous functionally graded deep beams. Effects of viscoelastic parameter, porosity parameter, graduation index on the dynamic behavior of porous functionally graded deep beams with viscoelastic core are investigated and discussed. Material damping and porosity have a significant effect on the forced vibration response under harmonic excitation force. Increasing the material viscosity parameters results in decreasing the vibrational amplitudes and increasing the vibration time period due to increasing damping effect. Obtained results are supportive for the design and manufacturing of such type of composite beam structures.

• Steel and Composite Structures
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• v.46 no.4
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• pp.471-483
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• 2023

This paper presents an analytical hyperbolic theory based on the refined shear deformation theory for mechanical stability analysis of the simply supported advanced composites plates (exponentially, sigmoidal and power-law graded) under triangular, trapezoidal and uniform uniaxial and biaxial loading. The developed model ensures the boundary condition of the zero transverse stresses at the top and bottom surfaces without using the correction factor as first order shear deformation theory. The mathematical formulation of displacement contains only four unknowns in which the transverse deflection is divided to shear and bending components. The current study includes the effect of the geometric imperfection of the material. The modeling of the micro-void presence in the structure is based on the both true and apparent density formulas in which the porosity will be dense in the mid-plane and zero in the upper and lower surfaces (free surface) according to a logarithmic function. The analytical solutions of the uniaxial and biaxial critical buckling load are determined by solving the differential equilibrium equations of the system with the help of the Navier's method. The correctness and the effectiveness of the proposed HyRPT is confirmed by comparing the results with those found in the open literature which shows the high performance of this model to predict the stability characteristics of the FG structures employed in various fields. Several parametric analyses are performed to extract the most influenced parameters on the mechanical stability of this type of advanced composites plates.

• Journal of Aerospace System Engineering
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• v.17 no.4
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• pp.126-132
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• 2023

Recently, the consideration of eco-friendly technology to reduce greenhouse gas is being emphasized in the aviation field. Various studies for applying electro-mechanical actuators that control mechanical linear and rotational movements using electricity as the primary power source are in progress. In this study, the fatigue analysis of the electro-mechanical actuator for the front wheel steering of a single aisle aircraft was carried out. A unit load stress table was constructed for the vulnerable part selected through structural analysis, and the representative stress for each load profile was calculated using the unit load stress table constructed for the vulnerable part. Then, individual profiles of representative stress group were extracted from continuous load profiles by applying the rainflow counting method. The damage of each profile was calculated by applying the S-N diagram. Finally, the total damage in the vulnerable parts was calculated by the linear cumulative damage law, and the fatigue life of the electro-mechanical actuator for the front wheel steering of a single aisle aircraft was evaluated.

• Structural Engineering and Mechanics
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• v.84 no.3
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• pp.423-435
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• 2022

In this article, we present torsion-bending analysis of a composite FGM beam with an open section, according to the advanced and refined theory of 1D / 3D beams based on the 3D Saint-Venant's solution and taking into account the edge effects. The (initially one-dimensional) model contains a set of three-dimensional (3D) displacement modes of the cross section, reflecting its 3D mechanical behaviour. The modes are taken into account depending on the mechanical characteristics and the geometrical form of the cross-section of the composite FGM beam. The model considered is implemented on the CSB (Cross-Section and Beam Analysis) software package. It is based on the RBT/SV theory (Refined Beam Theory on Saint-Venant principle) of FGM beams. The mechanical and physical characteristics of the FGM beam continuously vary, depending on a power-law distribution, across the thickness of the beam. We compare the numerical results obtained by the three-beam theories, namely: The Classical Beam Theory of Saint-Venant (Classical Beam Theory CBT), the theory of refined beams (Refined Beam Theory RBT), and the theory of refined beams, using the higher (high) modes of distortion of the cross-section (Refined Beam Theory using distorted modes RBTd). The results obtained confirm a clear difference between those obtained by the three models at the level of the supports. Further from the support, the results of RBT and RBTd are of the same order, whereas those of CBT remains far from those of higher-order theories. The 3D stresses, strains and displacements, obtained by the present study, reflect the 3D behaviour of FGM beams well, despite the initially 1D nature of the problem. A validation example also shows a very good agreement of the proposed models with other models (classical or higher-order beam theory) and Carrera Unified Formulation 1D-beam model with Lagrange Expansion functions (CUF-LE).

• Structural Engineering and Mechanics
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• v.86 no.2
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• pp.167-180
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• 2023

This work applies a four-known quasi-3D shear deformation theory to investigate the bending behavior of a functionally graded plate resting on a viscoelastic foundation and subjected to hygro-thermo-mechanical loading. The theory utilizes a hyperbolic shape function to predict the transverse shear stress, and the transverse stretching effect of the plate is considered. The principle of virtual displacement is applied to obtain the governing differential equations, and the Navier method, which comprises an exponential term, is used to obtain the solution. Novel to the current study, the impact of the viscoelastic foundation model, which includes a time-dependent viscosity parameter in addition to Winkler's and Pasternak parameters, is carefully investigated. Numerical examples are presented to validate the theory. A parametric study is conducted to study the effect of the damping coefficient, the linear and nonlinear loadings, the power-law index, and the plate width-tothickness ratio on the plate bending response. The results show that the presence of the viscoelastic foundation causes an 18% decrease in the plate deflection and about a 10% increase in transverse shear stresses under both linear and nonlinear loading conditions. Additionally, nonlinear loading causes a one-and-a-half times increase in horizontal stresses and a nearly two-times increase in normal transverse stresses compared to linear loading. Based on the article's findings, it can be concluded that the viscosity effect plays a significant role in the bending response of plates in hygrothermal environments. Hence it shall be considered in the design.

• Structural Engineering and Mechanics
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• v.81 no.2
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• pp.179-194
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• 2022

The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

• The Journal of the Acoustical Society of Korea
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• v.41 no.2
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• pp.174-183
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• 2022

Acoustic radiation from a submerged elastic shell with an internal fluid surrounded by the bubble layer is studied with the modal theory. An omni-directional point source located on the center of the internal fluid is used as acoustic noise source. The unknown coefficients of modal solutions are solved using the interface conditions between media. To preserve the stability of the modal solution over wide frequency ranges, the scaled technique of modal solution is used. The bubble layer is modeled with four kinds of bubble distribution; uni-modal distribution, uniform distribution, normal distribution, and power-law distribution, based on the effective medium theory of Commander and Prosperetti. For each bubble distribution, the insertion losses are mainly calculated for the frequency. In addition, the numerical simulations are performed depending in the bubble void fraction, the material property of elastic shell, and the gap between the bubble layer and the elastic shell.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.2
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• pp.50.3-51
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• 2021

The progenitor of Type Ia supernovae is largely expected as a close binary system of a carbon/oxygen white dwarf (WD) primary and its secondary non-degenerate (single degenerate; SD) or degenerate companion (double degenerate; DD). Here we present a high-cadence monitoring observation of SN 2021hpr in a spiral galaxy, NGC 3147. SN 2021hpr shows typical characteristics as a normal type Ia supernova from its photometric (Δm₁₅(B)=1.01±0.03, dust free M_B,max=-19.45±0.02) and spectroscopic data. To investigate its progenitor system, we fit the early part of BVRI-band light curve simultaneously with a combined version of ejecta-companion and simple power-law model. As a result, we found a significant feature of an early excess possibly from a 7.63±0.52R_⊙-sized companion at the optimal viewing angle while the fit is not successful at the common viewing angle. No possible red sources brighter than F555W=-7.01 AB mag is detected at the SN location in Hubble Space Telescope (HST) pre-explosion images, excluding massive stars with initial mass of >16M_⊙ as companions. We suggest the progenitor system of SN 2021hpr can be a fairly large companion such as a main sequence, a low mass subgiant, and a helium giant star. In addition, a possibility of the ejecta-Disk Originated Matter (DOM) interaction for the DD scenario considering linearly-rising early flux still remains.

• Steel and Composite Structures
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• v.47 no.5
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• pp.551-568
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• 2023

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.